Theorem orim2d 796

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 794	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 716

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 717

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  797  orbi2d  798  pm2.82  820  stdcndcOLD  854  pm2.13dc  893  exmid1dc  4296  acexmidlemcase  6023  poxp  6406  fodjuomnilemdc  7386  omniwomnimkv  7409  exmidontriimlem1  7479  indpi  7605  suplocexprlemloc  7984  nneoor  9626  uzp1  9834  maxabslemlub  11830  xrmaxiflemlub  11871  nninfctlemfo  12674  exmidunben  13110  bj-nn0suc  16663  sbthomlem  16736